The Floppiness of It All: Bond Lengths Change with Atomic Displacement Parameters and the Flexibility of Various Coordination Tetrahedra in Zeolitic Frameworks. An Empirical Structural Study of Bond Lengths and Angles

We have evaluated more than 7000 crystal structures of zeolites in terms of the values of their bond-lengths T–O (T = Si, Al, P, Zn, Be, Ge, B, As, Ga, Co) and their variability as well as the flexibility of their bond angles O–T–O. Out of these known crystal structure descriptions of zeolites, we have selected 1179 which have estimated standard deviations of their T–O bond lengths of 0.01 Å or less. For the most common bond lengths, we obtain 1.603(11) Å for 1323 mean tetrahedral Si–O, 1.736(8) Å for 416 Al–O, and 1.522(9) Å for 228 P–O. It is unsettling that the spread of each of these values is large: about 0.07 Å within the population studied by us. Furthermore, these values disagree by several hundredths of an Ångström from some of the mean values of Si–O, Al–O, and P–O compiled from nonzeolitic types of compounds. This is at variance with the widespread conviction that such T–O distance values should be relatively constant across different types of inorganic compounds. Ever since Cruickshank (Acta Crystallogr. 1956, 9, 757), it has been known that high atomic displacement factors shorten observed bond lengths. Corrections for this effect were applied in the past but have become lately rarer. We find that much of the variance observed by us in the bond lengths is due to the fact that topologically different zeolite framework types have different atomic displacement parameters of their oxygen atoms. Thus, it makes no sense to search for mean tetrahedral bond lengths in TO4 tetrahedra. Instead, a particular mean bond length, e.g., Si–O, can be only characteristic for a Si–O bond for one given framework type as we show for the topologically different framework types CAN, FER, MFI, NAT, and SOD. Even after bond length corrections for differing displacement parameters, the mean Si–O bonds range from 1.601 Å for FER to 1.629 Å for SOD. The observed angles O–T–O cover a range from 94.5 to 129.1° averaging around a tetrahedral angle of 109.5°. The largest deviations from the tetrahedral angle occur for tetrahedra with long mean T–O distances of the T-atoms. Our results, properly applied, can be useful as an input for distance least squares calculations on zeolites and for checking on the results of crystal structure refinements or of theoretical calculations.